1. Field of the Invention
The present invention relates to an exposure method and apparatus and, in particular, to an exposure method and apparatus in which a pattern of a mask or reticle is projected onto a substrate to be processed in a lithography step. Here, the lithography step is a step in a process for making semiconductor devices, imaging devices (CCD and the like), liquid crystal display devices, thin-film magnetic heads, semiconductor integrated circuits, and the like.
2. Related Background Art
When a semiconductor device, a liquid crystal display device, or the like is to be manufactured, in a photolithography step, used is a projection exposure apparatus such as stepper. The projection exposure apparatus projects and transfers, by way of a projection optical system, a pattern of a mask or reticle onto each shot area on a wafer, a glass plate, or the like which is coated with photoresist. In a semiconductor device, a number of layers of circuit patterns are formed on a wafer as being laminated on each other with a predetermined positional relationship. Accordingly, when the circuit pattern of the second or later layer is to be projected onto the wafer, it is necessary to accurately align the reticle pattern to be projected with each shot area on the wafer where a circuit pattern has already been formed. Therefore, the conventional projection exposure apparatus has been configured such that an alignment sensor detects the position of a wafer mark provided at a predetermined shot area (already formed chip pattern) and, based on the result of detection, performs alignment of the individual shot areas. Here, it is important to accurately perform the alignment with respect to the shot area and adjust the exposure apparatus.
Also, on the wafer, a number of shot areas are regularly arranged according to a preset arrangement coordinates, while each shot area has a chip pattern formed therein including an alignment mark used for alignment thereof. As a method of aligning a reticle pattern with a shot area of a wafer, enhanced global alignment method (referred to as "multipoint EGA method" or "EGA method" hereinafter) is disclosed, for example, in Japanese Patent Laid-Open No. 6-275496 (U.S. patent application Ser. No.08/254,524) and U.S. Pat. No. 4,780,617. In particular in the former document, magnification, rotation, or the like of a chip are also taken into consideration.
In the following, the alignment according to the multipoint EGA method will be explained. In this method, the arrangement coordinates of a shot to be aligned, magnification of the chip, rotation thereof, and the like are computed according to a statistical arithmetic technique assuming that errors between the measured positions of alignment marks respectively disposed at a plurality of points within the shot area and their designed positions are caused by the following factors (1) to (7):
(1) residual rotational error .THETA. of the wafer;
(2) orthogonality error W of a stage coordinate system (or shot arrangement);
(3) linear expansion or contraction Rx and Ry of the wafer;
(4) offset (translation) O.sub.x and O.sub.y of the center position of the wafer;
(5) residual rotational error .theta. of the chip pattern on each shot area of the wafer;
(6) orthogonality error w of a coordinate system (chip pattern) on the wafer; and
(7) linear expansion or contraction rx and ry with respect to two directions of the chip pattern orthogonal to each other.
Here, the error parameters .THETA., W, Rx, Ry, O.sub.x, and O.sub.y are defined with respect to the stage coordinate system (X, Y), whereas the error parameters .theta., w, rx, and ry are defined with respect to the coordinate system (x, y) of the shot area.
Assuming that the designed coordinate value of a reference point (e.g., shot center) on a coordinate system (.alpha.,.beta.) on the wafer in each of a plurality of shot areas selected on the wafer is C.sub.n, that the designed coordinate value (relative coordinate value) of the measured alignment mark in the coordinate system (x, y) on each shot area is S.sub.Nn, and that the calculated value of the alignment mark to be disposed on the stage coordinate system (X, Y) is F.sub.Nn, F.sub.Nn is represented by the following expression (1): EQU F.sub.Nn =AC.sub.n +BS.sub.Nn +O (1)
wherein the individual vectors and transformation matrices in the above expression are defined as shown in the following expression (2). Here, the residual rotational error .THETA. of the wafer, orthogonality error W, residual rotational error .theta. of the chip pattern, and orthogonality error w are linearly approximated assuming that they are of minute quantities; while approximation is performed by: EQU Rx=1+.GAMMA.x, Ry=1+.GAMMA.y, EQU rx=1+.gamma.x, ry=1+.gamma.y
assuming that .gamma.x, .gamma.y, .gamma.x, and .gamma.y are of minute quantities. ##EQU1##
Then, 10 error parameters (.THETA., W, .GAMMA.x, .GAMMA.y O.sub.x, O.sub.y, .theta., w, .gamma.x, and .gamma.y) satisfying expression (1) are determined by least square method. Specifically, the difference (E.sub.NXn, E.sub.NYn) between an actually measured coordinate value (FM.sub.NXn, FM.sub.NYn) and its calculated coordinate value (F.sub.NXn, F.sub.NYn) is considered to be an alignment error. Thus, EN.sub.NXn =FM.sub.NXn -F.sub.NXn, and EN.sub.NYn =FM.sub.NYn -F.sub.NYn. Also, the sum of squares of five or more sets of alignment errors (E.sub.NXn, E.sub.NYn), namely, 10 or more values of alignment errors, is partially differentiated with the above-mentioned 10 parameters in succession; equations are established so as to minimize the resulting differentiated values; and then these 10 simultaneous equations are solved by least square method; whereby the 10 error parameters can be determined.
Thereafter, the reticle is appropriately rotated or the wafer is rotated so as to correct the rotational error .theta. of the chip rotation in the above-mentioned transformation matrix B, thereby correcting the rotation of the chip pattern with respect to the stage coordinate system (X, Y). Though the orthogonality error w cannot be corrected in its strict sense, the error can be minimized when the reticle is appropriately rotated. Therefore, the amount of rotation of reticle or wafer can be optimized such that the sum of respective absolute values of the residual rotational error .THETA. of the wafer, residual rotational error .theta. of the chip pattern, and orthogonality error w is minimized.
Thereafter, the magnification of projection of the projection optical system is adjusted so as to correct the chip scaling errors .gamma.x and .gamma.y in the transformation matrix B. Subsequently, the transformation matrices A and O are used such that a designed arrangement coordinate value (C.sub.xn, C.sub.yn) of the reference point in each shot area is input into the following expression (3), so as to determine a calculated arrangement coordinate value (G.sub.xn, G.sub.yn) of the reference point on the stage coordinate (X, Y). ##EQU2##
Then, based on thus calculated arrangement coordinates (G.sub.xn, G.sub.yn) and a predetermined baseline amount, the reference point of each shot area on the wafer is sequentially aligned with a predetermined position within the exposure field of the projection optical system, and the pattern image of the reticle is projected onto the shot area. After all the shot areas on the wafer are exposed to the pattern image, a processing such as development of the wafer is effected.
According to the alignment of this multipoint EGA method, since not only the tranformation matrices A and O but also the transformation matrix B including the respective parameters for chip rotation, orthogonality error of the chip, and chip scaling is taken into account, influence of expansion and contraction, roration, or the like of the chip pattern itself which is transferred to each shot area can be minimized so that the chip pattern of each shot area on the wafer and the projected image of the reticle pattern are overlaid with each other more accurately.
In the alignment of the above-mentioned multipoint EGA method, alignment marks positioned at a plurality of points within a shot are measured in order to determine errors within the shot, i.e., parameters for chip rotation, orthogonality error of the chip, and chip scaling. The coordinate values of thus measured alignment marks, however, include errors caused by lens distortion in its alignment target layer exposure unit. Accordingly, when thus measured value is used as it is, while the reticle or wafer is rotated so as to correct the rotational error .theta. of chip rotation or the projection magnification of the projection optical system is adjusted so as to correct the chip scaling errors .gamma.x and .gamma.y, there have been problems that shot magnification errors or shot ratation errors occur.
Also, recently, in order to increase throughput (number of wafer sheets processed per unit time), different exposure apparatuses have been used respectively for different layers on the wafer so as to effect exposure in a mix-and-match method. In this case, when the magnification of the projection image of the projection exposure apparatus used for the exposure of the first layer on the wafer differs from that of the projection exposure apparatus used for the exposure of the second layer on the wafer, overlay accuracy deteriorates between these two layers. Accordingly, in order to improve the overlay accuracy, for example, a plurality of wafer marks disposed within a predetermined shot area on the wafer with a predetermined positional relationship, respectively indicating two-dimensional positions, have been detected so as to determine the linear magnification error of the pattern in the first layer within each shot area, whereby the magnification of the projection optical system of the projection exposure apparatus to be subsequently used has been corrected in response to this linear magnification error. Here, such a method in which positions of a plurality of wafer marks are detected within one shot area as being converted into two-dimensional marks has also been known as in-shot multipoint alignment measurement method.
As mentioned above, in the conventional exposure method of mix-and-match type, there have been cases where, upon exposure of the second layer in each shot area on the wafer, the magnification of the projected image is corrected in response to the magnification of the pattern of the first layer. Nevertheless, distortion (non-linear magnification error) characteristics in the projection exposure apparatuses used for exposure of these two layers have not been taken into account in particular. Therefore, when such distortion characteristics greatly differ from each other, the overlay accuracy between these two layers have disadvantageously deteriorated. This phenomenon will be explained with reference to FIGS. 12, 13A, and 13B.
FIG. 12 shows an example of distortion in a projected image in a conventional projection exposure apparatus. In this drawing, an image formed when a predetermined square original pattern is projected onto a wafer by way of a projection optical system, which is free of distortion and linear magnification error and has a predetermined magnification (e.g., 1/5), is depicted with dotted lines as a reference pattern 56; whereas an image formed when this original pattern is projected onto a first layer on the wafer by way of a projection optical system having a pin-cushion type distortion is depicted with continuous curves as a projection pattern 65. When the distortion characteristic of the projection pattern 65 is to be measured, amounts of positional deviation of the projection pattern 65 from its ideal position (reference pattern 56 in this case) are measured at four measurement points 57A to 57D respectively at the centers of the four sides of the reference pattern 56 and four measurement points 58A to 58D on four apexes of the reference pattern 56, for example. Then, the distortion characteristic of the projection pattern 65 is substantially specified by the amounts of positional deviation at these eight measurement points 57A to 57D and 58A to 58D or, desirably, more measurement points.
On the other hand, when positions of a plurality of wafer marks within a predetermined shot area on a wafer are detected by way of an alignment sensor according to the in-shot multipoint alignment measurement method, since there is not so much room for forming wafer marks within each shot area and there is necessity for shortening measurement time, positional detection of wafer marks is effected at only two or four measurement points, for example. Accordingly, as compared with the number of points required for specifying the distortion characteristic, the number of measurement points employed by the alignment sensor is considerably smaller, thereby making it difficult to perform correction in response to distortion.
Specifically, it is assumed that the projection optical system of the projection exposure apparatus used for exposing the second layer on the wafer to light is free of distortion and linear magnification error. Then, when the amounts of positional deviation of the wafer mark are measured at the four measurement points 57A to 57D on the reference pattern 56 in FIG. 12, the projection pattern judged from the result of this measurement becomes a small projection pattern 66 depicted in FIG. 13A. Accordingly, when exposure of the second layer is effected at a magnification corresponding to the projection pattern 66, the overlay error between the projection pattern 65 of the first layer and the projection pattern 66 of the second layer is made large.
Also, when the amounts of positional deviation of the wafer mark are measured at the measurement points 58A to 58D on the four apexes of the reference pattern 56 in FIG. 12, the projection pattern judged from the result of this measurement becomes a large projection pattern 67 depicted in FIG. 13B. Accordingly, when exposure of the second layer is effected at a magnification corresponding to the projection pattern 67, the overlay error between the projection pattern 65 of the first layer and the projection pattern 67 of the second layer is made large.
Thus, since distortion of projection lenses is not taken into account in the conventional exposure method, there have been problems that shot magnification error and shot rotation error may occur. Also, even when the in-shot multipoint alignment measurement method is adopted, there has been an inconvenience that the overlay accuracy between two layers on the wafer may greatly fluctuate upon positions and number of measurement points employed by the alignment sensor.